Question

A vector has an x-component of length 12 and a y-component of length 14.

What is the angle of the vector? (Hint: Use the inverse tangent.)

Answer 1

∴ The angle of the vector is 49.4°.

Step-by-step explanation:

Given:

For a vector:

`x-component\rightarrow 12`

`y-component\rightarrow 14`

The tangent of angle of a vector is given by:

`\tan \theta=(y)/(x)`

where
`\theta` represents the angle of the vector,
`y` represents the length of
`y-component` and
`x` represents the length of
`x-component`.

Plugging in the given values to get the angle of vector
`\theta`.

`\tan \theta=(14)/(12)`

Taking
`\tan^(-1)` both sides to get
`\theta`

`\theta=\tan^(-1)(14)/(12)`

`\theta=49.4\°`

∴ The angle of the vector is 49.4°.